I think I figured out where Ayn Rand had it wrong. You cannot be saved on Principle alone. That is why the Gospel is so great! After listening to conference talks with a new "abundant" ear, I can hear the principles taught over and over. The Church is not just a club, it is the true principles with the saving ordinances which help us become who we were meant to become!
At some point, principled people will realize that they do not have what it takes alone to return to the God who created them and who is the Author of their Prosperity. This, to me, seems like a logical reason for why Ayn Rand was agnostic. If she admitted that saving ordinances existed, then she would know that she didn't have them and she would thus live an unfulfilled life. Because she tried to remove principle 1, she deceived herself into thinking she had reached true happiness. Although I believe that she did receive a huge amount of happiness maybe even more happiness than many members of the True Church. If this is the case, which I believe it is, it proves that the Saving ordinances without the principles are not enough either. You must follow both to receive the full measure of happiness.